5
Select the correct answer.
If the domain of the function, f, is restricted to x 20, which function is the inverse off?
f(x) = 91² - 12, 20
O A. q(z) = √2+1
√√2-12
3
OB. h(z)
OC. p(z) = √2-12
c.
9
√2+12
D. g(x)
O D.

The monomials in the expression are given as follows:

x², xy, -8y².

The simplified polynomial is given as follows:

9x² + 9xy - 72y².

With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.

The expression for this term are given as follows:

9(x² + xy - 8y²).

The inner term is a polynomial composed by the sum/subtraction of the monomials presented as follows:

x², xy, -8y².

Applying the distributive property, the simplified polynomial is given as follows:

9x² + 9xy - 72y².

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When someone aged 20 sets up an IRA retirement account with an APR of 5% and deposits $65 at the end of each month, when he retires at age 65, the account will have a future value of $131,718.42.

b) Compared to the total deposit he made over time ($35,100.00), he generated a total compounded interest of $96,618.42.

The future value can be determined using an online finance calculator, which compounds the interest at 5% over a period of 540 months or 45 years.

Number of years = 45 years (65 - 20)

N (# of periods) = 540 months (45 years x 12)

I/Y (Interest per year) = 5%

PV (Present Value) = $0

PMT (Periodic Payment) = $65

Results:

Future Value (FV) = $131,718.42

Sum of all periodic payments = $35,100.00 ($65 x 540 months)

Total Interest = $96,618.42

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The students' line that will be parallel to line d is the line with the same slope as d

The rules are given as

This means that the equations of the function are

Carly: y = x + 2

Ramil: y = 2x + 1

If the slope of line d is 1, Carly's line will be parallel to line d and if the slope of line d is 2, Ramil's line will be parallel to line d

This is because parallell lines have equal slopes

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The expression [tex]V^2 (V^2_Z)[/tex] is called mean-square speed.

In Mathematics and Science, mean-square speed is sometimes referred to as root-mean-square speed and it can be defined as a measure of the average value of square-speed of particles that are found in a molecule, gas, or liquid.

Mathematically, the mean-square speed of any particle is denoted or represented by this expression [tex]V^2 (V^2_Z)[/tex].

This ultimately implies that, mean-square speed is always calculated as the square root of the average value of the squares of the speeds (velocities) of each particles in thermodynamics and kinetic theory of gases.

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Complete Question:

The expression [tex]V^2 (V^2_Z)[/tex] is called ______?

The name of the shape Kimberly forms by connecting the points is a plane shape

From the question, we have the following parameters that can be used in our computation:

A shape is formed by connecting points

As a general rule; shapes formed by connecting points are referred to as plane shapes, and examples of them are:

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The correct answer is 3. Response and non-response bias.

Response bias occurs when the way that questions are asked or worded, or the context in which they are asked, influences how respondents answer them. This can lead to inaccurate or incomplete information being collected.

Non-response bias occurs when some individuals selected to participate in a survey do not respond. This can happen for various reasons, such as being unavailable, unwilling, or unable to participate. Non-response bias can skew the results of a survey because the characteristics of those who do not respond may differ from those who do respond.

In this scenario, the principal has asked all math and English teachers to rank his school leadership on a scale of 1 to 10. If some teachers do not respond to the survey or are unavailable, unwilling, or unable to participate, this could lead to non-response bias.

Additionally, if the principal has a reputation for being well-liked or well-respected, some teachers may feel pressured to give a higher rating than they otherwise would, which could lead to response bias.

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The value of the length x is 2√70. Option C

To determine the value of the length of the triangle, we need to consider the different trigonometric identities, they are;

Now, using the Pythagorean theorem, we have;

17² = x² + 3²

Find the square values and substitute

289 = x² + 9

collect the like terms

x² = 289 - 9

Subtract the values

x² = 280

Find the square root of both sides

x = √280

Find the values

x = √4× 70

x = 2√70

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Part(A),

The value of the mean is 27.1, the value of the mode is 12 and median is 27.5.

Part(B),

Tennis players should report the median value to show they are less prepared for the tournament.

Part A:

To calculate the mean, we need to find the sum of all the data values and divide by the total number of values:

Sum of the data = 12 + 12 + 29 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 271

Number of data values = 10

Mean = sum of the data/number of data values

Mean = 271 / 10

Mean = 27.1

Therefore, the mean time spent practicing is 27.1 minutes.

To find the median, we need to arrange the data in order from smallest to largest:

12, 12, 20, 22, 26, 29, 31, 31, 40, 68

There are 10 data values, so the median is the average of the two middle values:

Median = (26 + 29) / 2

Median = 27.5

Therefore, the median time spent practicing is 27.5 minutes.

To find the mode, we need to identify the data value that occurs most frequently. In this case, there are two modes:

Mode = 12 and 31

Therefore, the modes for the time spent practicing are 12 and 31 minutes.

To find the range, we need to subtract the smallest data value from the largest data value:

Range = largest data value - smallest data value

Range = 68 - 12

Range = 56

Therefore, the range of time spent practicing is 56 minutes.

Part B:

Based on the scenario, it is more appropriate for the tennis players to report the median value to show they are less prepared for the tournament. This is because there is one outlier value of 68, which is much larger than the other data values.

The mean is affected by outliers and may not represent the typical amount of time spent practicing for the tournament. On the other hand, the median is not affected by outliers and represents the middle value of the data set, which is a more accurate measure of the typical amount of time spent practicing.

Therefore, tennis players should report the median value to show they are less prepared for the tournament.

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Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

We know that,

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

To find out how many projects Mrs. Kenny can complete with 7/8 pound of clay, we need to divide 7/8 by 1/6:

= (7/8) ÷ (1/6)

To divide fractions, we need to invert the second fraction and multiply:

= (7/8) × (6/1)

Simplifying the fractions, we get:

(7 × 6)/(8 × 1) = 42/8 = 5 1/4

Thus, Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

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The number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

Using the sine rule;

29/sin20° = 32°/sinT

T = (33 × sin20°)/29° {cross multiplication}

m∠T = 23 {to the nearest degree}

m∠S = 180 - (20 + 23)° {sum of interior angles of a triangle}

S = 127°

Therefore, the number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.

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The measure of angle 3 is 95°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

When we have two parallel lines and they are intersected by a transversal , the angles on the parallel lines are corresponding and equal.

Therefore angle 3 = angle 7

angle 7 = 180-(angle 6) (angles on a straight line)

angle 7 = 180-85

= 95°

angle 3 = angle = 7 = 95°

Therefore the value of angle 3 is 95°

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Part(2),

The volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.

Part(3),

The difference in price per cubic inch is $0.0128/in³.

Part(4),

The volume of the cylinder with a radius of 8 inches and a height of 6 inches.

Part(2)

The volume of a cone is given by the formula V = (1/3)πr²h,

where r is the radius and h is the height. The volume of the snowcone is therefore V = (1/3)π(4 cm)²(12 cm) = 201.06 cubic cm.

V = (1/3)π(3 cm)²(12 cm) = 113.1 cubic cm.

Since the volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.

Part(3)

To compare the cost per cubic inch of the two sizes of cereal boxes, we need to calculate the volume of each box and divide the cost by the volume.

The volume of the family-sized box is V = 3 in x 9 in x 12 in = 324 cubic inches.

The cost per cubic inch is therefore $6/324 in³ = $0.0185/in³.

The volume of the regular-sized box is V = 2 in x 8 in x 9 in = 144 cubic inches. The cost per cubic inch is, therefore, $4.50/144 in³ = $0.0313/in³.

The difference in price per cubic inch is $0.0313/in³ - $0.0185/in³ = $0.0128/in³.

Part(3)

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

For the cylinder with a radius of 6 inches and a height of 8 inches, the volume is V = π(6 in)²(8 in) = 904.78 cubic inches.

For the cylinder with a radius of 8 inches and a height of 6 inches, the volume is V = π(8 in)²(6 in) = 1206.37 cubic inches.

Therefore, the volume of the cylinder with a radius of 8 inches and a height of 6 inches.

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a. The error is that the two factors should be 5s and 3s-7s²+1

b. The student out to multiply the two factors if the product will be 15s²-35s³+5s

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors.

For example, if we are given an expression , 2x +6. The expression consist of two terms and the common factor between them is 2 . Therefore we bring the 2 out . i.e 2( x+3). This means the two factors are 2 and x+3

Similarly , 15s²-35s³+5s can be factorized by bring out the common factors between the three terms

= 5s( 3s-7s²+1)

This means that the student omitted +1 and she ought to have cross checked by multiplying the two factors back if the product will be the polynomial.

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Answer:

Step-by-step explanation:

The rule for a triangle is that if you add the 2 shorter sides, it must be greater than the longest side (can't even be =, must be bigger.

A.  36+48>60 true yes triangle

B   6.2+5.7>9.4 yes triangle

C.  20+20 is not greater than 50 no not at triangle

D.  12+24>32 yes triangle

Vertical angles mean angles across from each other when 2 lines intersect.

So:

B, C, D  are vertical angles

A relation is called a function when each element in the domain is paired with just one element from the A. Range

From the question, we have the following parameters that can be used in our computation:

The incomplete definition of relation

A relation takes the form

Domain : x

Range : y

The values from the domain are then paired with the range

If these values are paired just once, then it is a function

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The amount that was initially deposited is obtained as $10,100.

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods.

The interest earned in each subsequent period is added to the principal, and the interest is then calculated on the new, larger amount.

We have that;

A = P (1 + r/n)^nt

Then we have;

A = amount

P = principal

r = rate

n = number of times compounded

t = time in years

Then;

14,472.74 = P(1 + 0.055/12)^12 * 5

P = $10,100

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The amount of tape that Abigail will use to cover the jewelry box is given as follows:

298 in².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The dimensions of the box are given as follows:

6 in, 12.5 in and 4 in.

Hence the amount of tape, given by the surface area, is obtained as follows:

S = 2 x (6 x 12.5 + 6 x 4 + 12.5 x 4)

S = 298 in².

The dimensions of the box are given as follows:

6 in, 12.5 in and 4 in.

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The number of bows can Sydney make are 3, we get by division.

Given that Sydney has [tex]1\frac{1}{5}[/tex] yards of ribbon to make bows

Each bow is made from a piece of ribbon that is 2/5 yard long

We have to find the number of bows can Sydney make

To find this we have to divide the total length of ribbon by 2/5

[tex]1\frac{1}{5}[/tex]/(2/5)

6/5×5/2

We get 3

Hence, the number of bows can Sydney make are 3

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The product of the matrices is [24].

Given is a row matrix and a column matrix, we need to find the product of both,

So,

A = [-3, 3, 0]

B = [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]

Now, the product will be =

AB = [-3, 3, 0] ×  [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]

AB = [9 + 15 + 0]

AB = [24]

Hence the product of the matrices is [24].

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The graph of f(x) relate to its parent function by B. The parent function has been translated up.

Given that

f(x) = 3x +2 +4

When evaluated, we have

f(x) = 3x + 6

The parent function of the above is

f(x) = 3x

When f(x) = 3x is compared to f(x) = 3x + 6, we have

Difference = 6

This means that the parant function is translated up by 6 units

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Answer:

Step-by-step explanation:

The area of a parallelogram with the given base and height is 96 square units.

Given that, x=4 units, y=12 units, and h=8 units.

From the given figure,

Area of parallelogram = Base×Height

Here, b=4+12 =16 units and h=8 units

Now, area of parallelogram = 16×8

= 96 square units

Therefore, the area of a parallelogram with the given base and height is 96 square units.

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After the vertical stretch by factor 3 the function becomes g(x)=3x².

The given function is f(x)=x² is vertically stretched by the factor 3.

When we stretch a function vertically, we multiply the base function by its scale factor. Hence, we have g(x) = 3·f(x). Let’s make sure to distribute 3 to each of the term in f(x).

Here, g(x)=3×x²

g(x)=3x²

Therefore, after the vertical stretch by factor 3 the function becomes g(x)=3x².

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Answer:

V = π(5.1^2)(7.1) + (1/3)π(5.1^2)(8.6)

= 184.671π + 74.562π

= 259.233π cubic feet

= about 814.4 cubic feet

m∡RST angle is 146 degrees and m∡RUT is 157 degrees are the arc measures.

Let us find angle RVT

The sum of four angles should be 360 degrees

∠RVS +∠SVU+∠UVT+∠RVT=360

64+139+75+x= 360

278+x=360

x=360-278

x=82 degrees

Arc measure m∡RST =64+82

m∡RST = 146 degrees

m∡RUT = 82+75

m∡RUT = 157 degrees

Hence, m∡RST is 146 degrees and m∡RUT is 157 degrees are the arc measures.

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Answer:

The answer is

13)CE

14)EG

15)BD

16)BF

The proportion when completed for the triangles is a/c = h/b

From the question, we have the following parameters that can be used in our computation:

The right triangles

The first expression in the proportion is a/c

This proportion represents leg/hypotenuse expression

Using this as a guide, we can make use of the following proportion

h/b

So, the complete equation is a/c = h/b

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Answer: Therefore, the probability of not landing on blue when spinning the spinner once is 62.5%.

Step-by-step explanation:  There are 8 sections on the spinner, and 3 of them are blue. Therefore, the probability of landing on blue is:

P(blue) = 3/8 = 0.375

The probability of not landing on blue is the complement of the probability of landing on blue:

P(not blue) = 1 - P(blue) = 1 - 0.375 = 0.625

To convert this probability to a percentage, we can multiply by 100:

P(not blue) = 0.625 x 100% = 62.5%